CBSE BOARD X, asked by jitendragupta5846, 1 year ago

In what ratio does y axis divide the join of (-2,1) and (4,5)? Find the coordinates of the point of intersection

Answers

Answered by bhakti3342
45
therefore
(X,Y) is (0,7/3)
hope this will help u
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Answered by JeanaShupp
29

Ratio = 1:2

Point of intersection = (0,\dfrac{7}{3})

Explanation:

Equation of line passing through (a,b) and (c,d) =(y-b)=\dfrac{d-b}{c-a}(x-a)

Then, Equation of line passing through (-2,1) and (4,5)=(y-5)=\dfrac{5-1}{4-(-2)}(x-4)

(y-5)=\dfrac{4}{6}(x-4)

(y-5)=\dfrac{2}{3}(x-4)

Put x=0

(y-5)=\dfrac{2}{3}(0-4)

y-=\dfrac{-8}{3}+5=\dfrac{7}{3}

(0,\dfrac{7}{3}) is the intersection point of line joining (-2,1) and (4,5) and y-axis.

Let the ratio be k:1.

Section formula : when a point P divides a line segment AB with endpoints A(x_1,y_1) and B (x_2,y_2) in m:n , then the coordinates of p is given by :-

x=\dfrac{mx_2+nx_1}{m+n}\\\\ y=\dfrac{my_2+ny_2}{m+n}

Then,

For given situation, we have

0=\dfrac{k(4)+1(-2)}{k+1}\\\\\Rightarrow\ 4k-2=0\\\\\Rightarrow\ k=\dfrac{1}{2}

k:1=\dfrac{1}{2}:1\\\\=1:2

Thus , the y axis divides the join of (-2,1) and (4,5) in ratio 1:2.

Learn more:

Find the coordinates of the point of intersection of the lines x+2y and 3x+4y=1​

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